Benchmark Review

Systems

100

_{Solve the system of equations.}

_y=2x+1

_y=x+4

(3,7)

200

Solve the system of equations. 

3x+2y=12

3x-2y=4

(8/3,2)

300

A movie theater sells adult tickets for $8 and student tickets for $5. A total of 10 tickets were sold for $62.

Which system of equations could be used to find the number of adult tickets a and student tickets s?

a+s=10

8a+5s=62

400

Two lines are graphed on a coordinate plane and intersect at the point (3, -1).

What does the point (3, -1) represent in the context of a system of equations?

The point (3, -1) represents the solution to the system, meaning it is the values of x and y that make both equations true.

500

Solve the system. 

y=-2x+6

4x+2y=12

Infinite solutions

Functions

100

Is this a function? 

(1,4), (2,7), (3,10), (4,13)

Yes

200

y=-3x+5

What is the slope and y-intercept? 

Slope is -3

Y-intercept is 5

300

A gym charges a $20 sign-up fee and $15 per month.

Write a function rule to represent the total cost C after m months.

y=15x+20

400

Function A: y=4x+1

Function B: (0,3), (1,9), (2,15), (3,21)

Which has the greatest rate of change?

Function B

500

y=2x^2 -3

29

Pythagorean Theorem

100

A right triangle has legs that measure 6 inches and 8 inches.

What is the length of the hypotenuse?

10 inches

200

A right triangle has a hypotenuse of 13 cm and one leg that measures 5 cm.

What is the length of the other leg?

12 cm

300

A ladder leans against a wall. The bottom of the ladder is 9 feet from the wall, and the ladder reaches 15 feet up the wall.

How long is the ladder?

The ladder is approximately 17.5 feet long

400

The side lengths of a triangle are 7, 24, and 25. Is this a right triangle?

Yes, it is a right triangle

500

Point A is located at (2, 3) and point B is located at (8, 15).

What is the distance between points A and B?

≈ 13.4 units

Solving Equations

100

3(2x - 5) = 4(x + 1)

x=19/2

200

5x + 7 - 2x = 3x + 1

7=1

no solution

300

 x/3 +2 =x/6 +5 

x=18

400

2(3x - 4) + 5 = 4x + 7

X=5

500

4(x - 2) + 6 = 4x - 2

4x-2=4x-2

Infinite solutions

Linear/Non-Linear

100

Which of the following is a linear equation?

A. y = 3x + 5

B. y =  x^6 +4 

C. y =  sqrt x +2 

D. y =  1/x +7 

A: 3x+5

200

(0,2), (1,4), (2,6), (3,8)

Are these linear or non linear? 

Linear, rate of change is constant

300

A graph is a curve that gets steeper as x increases. Is the function linear or non-linear?

Non-linear because linear lines are straight

400

A car rental company charges $40 per day plus a one-time fee of $100. Is the function describing total cost linear or nonlinear?

Linear, constant increase of $40

500

Which of these is nonlinear?

A. 2x+5y=10

B. y=3x-7

C. y=  x^3 +2 

D. 4x-y=8

C due to  x^3